Question

A motorbike manufacturing company manufactures X and Y parts. While manufacturing X, 15 out of 120 parts are likely to be defective. Similarly, 6 out of 90 are likely to be defective while manufacturing part Y. What is the probability of selecting a non-defective bike?

• A. $\frac{49}{120}$
• B. $\frac{49}{60}$
• C. $\frac{1}{120}$
• D. $\frac{7}{60}$

Answer 1

The correct option is B $\frac{49}{60}$

In the process of manufacturing X, 15 out of 120 parts may be defective.

Probability of part X being defective $=\frac{15}{120}$

Probability of X not being defective $=1–\left(\frac{15}{120}\right)=\frac{105}{120}$

Similarly, probability of the part Y being defective $=\frac{6}{90}=\frac{1}{15}$

Probability of Y not being defective
$=1–\left(\frac{1}{15}\right)=\frac{14}{15}$

Now, the assembled product will not be defective if both the parts are not defective. Hence, the probability of this event

$=\frac{105}{120}\times \frac{14}{15}=\frac{7\times 7}{60}=\frac{49}{60}$
[By using the multiplication theorem]